For example, in field theory commutativity holds for measurements or field interactions at space-like separation, and this is in general how causality is recovered there [1]}The simplest illustration of this is the commutation of the Klein-Gordon field operators
\(\phi (x)\)  and \(\phi (y)\)  at space-like separated \(x\)  and \(y\) ,
\( [\phi (x),\phi (y)] = 0 .\) 
Such a commmutation condition is also referred to in field theory as the locality postulate [2]}..
Motivated by this, we here take the commutation of actions in space-like separated regions as a fundamental building block in deriving agents that are secret relative to each other. Note that in particular, finding commuting sets of transformations in \(\mathcal {T}\)  is something that can be done prior to definitions of local agents; this is shown explicitly in Ref. [3]}. Commutation relations result in a nice algebraic structure — a lattice — in the space of transformations [3]}. This is also the case for the von Neumann bicommutant in operator algebras [5]}. Commutation is also an operational property of the theory: for example, commutation is independent of the choice of reference frames in relativity and quantum field theory [1]}, [2]}.
If two agents commute, secrecy follows from simpler conditions.
